I'm really on the fence with Jaime and Cersei being Targs, but completely against Tyrion being a Targ
I'm against both, but Tyrion is the least likely of the two. Here's what I'm basing it off.
Tywin was reportedly pissed at some of the liberties that Aerys took during the bedding, could possibly have led to the twins. But, if and it is a big if, Aerys did impregnated her, wouldn't he think there was a possiblity that the twins were his. Tywin's only other child was deformed dwarf that killed his mother at birth.
So if Aerys had been the father, keeping with Targ tradition, he wouldn't have been opposed to Cersei & Rhaegar's marriage. There is nothing he would have liked more than to have his son (with one woman) marry his daughter (with another woman). Plus his grandchild not Tywin's would sit on the Iron Throne & Casterly Rock.
As far as Tyrion, is there any indication that Joanna ever went to King's Landing just prior to her death? Tyrion was born in Casterly Rock and the mad King never left King's Landing.